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Single Idea 24301

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite]

Full Idea

Now if we would be willing to subtract, in thought, the very least we can from these multitudes, must not that which is subtracted, too, be a multitude and not one, if it doesn't partake of the one?

Gist of Idea

If we subtract a part from a multitude, will that part not itself be a multitude?

Source

Plato (Parmenides [c.366 BCE], 158c)

A Reaction

This seems to be remarkably close to Dedekind's famous and widely accepted definition of infinity in Idea 9826.

Book Reference

Plato: 'Parmenides', ed/tr. Gill,M.L./Ryan,P. [Hackett 1996], p.166

Related Idea

Idea 9826 A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]